Time-dependent resonance-fluorescence spectrum of two-level atoms: Sensitivity to the functional form of the strong laser pumping fields

Abstract

The responses of the time-dependent resonance fluorescence spectra of two-level atoms in the presence of (a) strong cw laser fields and (b) short pulsed laser fields to functional disturbances in these fields have been studied by the use of functional-sensitivity-analysis techniques. For the cw case, the transient and steady-state response regions are explored separately. It is found that the response to the field disturbance occurring during the earlier transient period is most prominent at the positions of the well-known three peaks of the corresponding spectrum. In contrast, the response to a disturbance taking place in or near the steady-state region tends to increase the separation between the peaks and lower the intensity of the line center, in exact agreement with the direct calculation of the perturbed spectrum. For the pulsed case, the response to the disturbance is most visible at the line center and at the accompanying multiple peaks caused by the population oscillation of the upper atomic level. The response strongly depends on the magnitude of the pulse area, thus giving rise to distinct asymptotic behavior for (2n+1)\ensuremath{\pi} and 2n\ensuremath{\pi} pulses. As the pulse area becomes large enough to cause significant population oscillation of the upper atomic level, the response of the spectrum shows a resemblance to that of the cw case.